Should I add a sun lamp when using an hdri environment?
Depends how your hdr looks like. If there is a bright light source, then you might increase contrast for the hdr. 

Standard setup gives result like this:



If you increase a contrast:



You can multiply or perform any other mathematical operation to get the brightness and the contrast you like.

Also if you'd like to keep the background plate with the original colors, you could mix in original, unchanged background like this: